Bojan Banjac

A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions

In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873], using a method for proving inequalities of mixed trigonometric polynomial functions.

Some Notes on a Method for Proving Inequalities by Computer

In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions, we demonstrate that the considered method generally in practice becomes one heuristic for the verification of inequalities. We give some improvements of the inequalities considered in the theorems for which the existing proofs have been based on the numerical verifications of Remez algorithm.

A proof of an open problem of Yusuke Nishizawa for a power-exponential function

This paper presents a proof of the following conjecture, stated by Nishizawa in [Appl. Math. Comput. 269, (2015), 146--154.]: for

Visualization of Weber's curves and surfaces with applications in some optimization problems

\displaystyle 0 \! \left(\frac{2}{\pi} + \frac{\pi\!-\!2}{\pi^{3}}(\pi^{2}\!-\!4x^{2})\right)^{\theta(x)}\!

A computer verification of a conjecture about the Erdös-Mordell curve

holds, where

Some applications of λ-method for obtaining approximations in filter design

\displaystyle \theta(x) \! = \! -\frac{(48\!-\!24\pi\!+\!\pi^{3})x^{3} }{3(\pi\!-\!2)\pi^{3}}+\frac{\pi^{3}}{24(\pi\!-\!2)}.

A Proof of an Open Problem of Yusuke Nishizawa

In this paper, we present a Java application for visualization of Webers curves and surfaces generated by at most 3 foci, directrix lines or planes.

Application of polynomial texture mapping in process of digitalization of cultural heritage.

In this paper we consider Erdös-Mordell inequality and its extension in the plane of triangle to the Erdös-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one conjecture that relates to Erdös-Mordell curve.

A method for extraction of arcs of the algebraic curves

In this paper some applications of λ-method of Mitrinović-Vasić for obtaining approximations in filter design. Some approximations of functions based on cardinal sine functions are given, and also example of an method for obtaining similar approximations for other functions.